I am a proud owner of a white Toyota Celica from 1990. I have it for a year now but
for the first time it start to have a problem.

Since some months there is sometimes a bit of resistance on the steering wheel. Did not really bother me at all but since a month
there is sometimes a lot more resistance on the steering wheel(maybe powersteeering) and evey now and then the engine shuts when I am standing still. Can't start the engine after this appears. When I try to restart the engine there is somekind of rattling sound... I renewed the belt and thigten it.

The power steering pump has a dedicated belt. Tension is controlled by the position of the pump. Loosen the pump and check that the pulley / pump turn "freely" with some minor resistance. If not, pump may need rebuild/replacement.

I had similar binding issues when the universal joint on the intermediate shaft between the rack and the firewall rusted up. I ended up replacing it with a junk yard part but it could have probably been saved by soaking it in penetrant oil to loosen in up and then coating with automatic transmission fluid with leaves a protective lubrication film. Maybe sure your intermediate shaft universal joint moves easily. You may need to get the shaft off to investigate it. Easy way to investigate is that with front wheels off the ground and the engine off, the steering should move smoothly left to right.

The loss of operation periodically sounds like a Fuel Pump problem. The Fuel Pump has been working for 31-years, so check this out. I would recommend you buy a new one and just replace the old one.
The basis for my opinion is that you have described what happens when you "run out of gas". When the Fuel Pump goes, that same effect is mimicked.